Details

analyze1.2s (9.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
25%	74.9%	0.1%	8
54.6%	45.2%	0.1%	9
56.2%	43.7%	0.1%	10
62.4%	37.4%	0.1%	11
65.9%	33.9%	0.1%	12
66.3%	33.5%	0.1%	13
69%	30.8%	0.1%	14

Compiler

Compiled 17 to 15 computations (11.8% saved)

sample202.0ms (1.6%)

Algorithm

1×

intervals

Results

138.0ms	123×	body	1280	valid
38.0ms	60×	body	640	valid
7.0ms	17×	body	320	valid
6.0ms	49×	body	80	valid
2.0ms	7×	body	160	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify163.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (147.0ms)

Iter	Nodes	Cost
0	5171	26

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 4.4b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
4.0b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
25×	`sqrt-prod_binary64`
24×	`times-frac_binary64`
16×	`unpow-prod-down_binary64`
10×	`distribute-lft-out_binary64`
8×	`associate-/r*_binary64` `add-exp-log_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`associate-/l*_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 106

Calls

4 calls:

15.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
10.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

series527.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

303.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
170.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
27.0ms	(pow.f64 (sin.f64 kx) 2)
26.0ms	(pow.f64 (sin.f64 ky) 2)

simplify125.0ms (1%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4942	2355
1	4942	2355

prune181.0ms (1.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	107	11	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	11	119

Merged error: 3.5b

Counts

119 → 11

Compiler

Compiled 2910 to 1657 computations (43.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
4.0b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite51.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

180×	`times-frac_binary64`
150×	`*-un-lft-identity_binary64`
99×	`add-sqr-sqrt_binary64`
98×	`add-cube-cbrt_binary64`
65×	`sqrt-prod_binary64`
32×	`unpow-prod-down_binary64`
28×	`associate-/r*_binary64`
26×	`distribute-lft-out_binary64`
17×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
7×	`div-exp_binary64`
6×	`pow-unpow_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`pow-to-exp_binary64` `1-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rec-exp_binary64` `pow-exp_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64` `flip-+_binary64`

Counts

4 → 193

Calls

4 calls:

20.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
10.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(pow.f64 (sin.f64 kx) 2)
4.0ms	(pow.f64 (sin.f64 ky) 2)

series517.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

299.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
165.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
26.0ms	(pow.f64 (sin.f64 ky) 2)
26.0ms	(pow.f64 (sin.f64 kx) 2)

simplify206.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (144.0ms)

Iter	Nodes	Cost
0	4931	5705
1	4931	5705

prune312.0ms (2.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	205	11	216

Merged error: 3.5b

Counts

216 → 11

Compiler

Compiled 5691 to 3350 computations (41.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (pow.f64 (sin.f64 ky) 2)))
14.6b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
14.6b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
14.6b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`unpow-prod-down_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`unpow2_binary64` `pow1/3_binary64` `sqr-pow_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 67

Calls

4 calls:

23.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))

series657.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (pow.f64 (sin.f64 ky) 2)))
163.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
162.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
162.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))

simplify135.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4884	1100
1	4884	1100

prune134.0ms (1.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	79	11	90

Merged error: 3.5b

Counts

90 → 11

Compiler

Compiled 2683 to 1623 computations (39.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.4b	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.0b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite50.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`sqrt-prod_binary64`
56×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
33×	`times-frac_binary64`
32×	`add-cube-cbrt_binary64`
15×	`unpow-prod-down_binary64`
12×	`distribute-lft-out_binary64`
11×	`associate-/r*_binary64`
8×	`sqrt-div_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`flip3-+_binary64` `pow-unpow_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-to-exp_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-exp_binary64`

Counts

4 → 117

Calls

4 calls:

17.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
12.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(pow.f64 (sin.f64 kx) 2)

series710.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

362.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
163.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
156.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
29.0ms	(pow.f64 (sin.f64 kx) 2)

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5040	3263

prune377.0ms (3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	129	11	140

Merged error: 3.5b

Counts

140 → 11

Compiler

Compiled 4763 to 2842 computations (40.3% saved)

regimes230.0ms (1.8%)

Compiler: Compiled 2172 to 1806 computations (16.9% saved)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	29
1	20	29

end0.0ms (0%)

sample6.5s (51.9%)

Algorithm

1×

intervals

Results

4.0s	3748×	body	1280	valid
1.4s	2040×	body	640	valid
307.0ms	682×	body	320	valid
169.0ms	1230×	body	80	valid
96.0ms	300×	body	160	valid

Compiler

Compiled 300 to 250 computations (16.7% saved)

Details

analyze1.2s (9.8%)

sample202.0ms (1.6%)

simplify163.0ms (1.3%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite37.0ms (0.3%)

series527.0ms (4.2%)

simplify125.0ms (1%)

prune181.0ms (1.4%)

localize15.0ms (0.1%)

rewrite51.0ms (0.4%)

series517.0ms (4.1%)

simplify206.0ms (1.6%)

prune312.0ms (2.5%)

localize19.0ms (0.1%)

rewrite34.0ms (0.3%)

series657.0ms (5.2%)

simplify135.0ms (1.1%)

prune134.0ms (1.1%)

localize18.0ms (0.1%)

rewrite50.0ms (0.4%)

series710.0ms (5.7%)

simplify88.0ms (0.7%)

prune377.0ms (3%)

regimes230.0ms (1.8%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample6.5s (51.9%)

Profiling